arXiv subjects
Publications and source records attributed to Lech Jakobczyk.
We present the complete solution of the problem of determination of trace-norm geometric discord for arbitrary two-qubit state. Final answer is achieved due to effective reduction of the problem to the study of critical points of certain mapping depending on projectors. Our results are illustrated on various, also new, families of two-qubit states and compared to already known special solutions.
We study the measurement-induced geometric discord based on the trace norm and generalize some properties known for qutrits to qudits. Previous preliminary results for bipartite qutrit systems (i.e. d=3 systems) are here strictly proved for arbitrary d. Present study supports observations, coming also from other approaches, that systems with $d \geq 3$ show similar behaviour when quantum correlations are concerned, but there is pronounced difference between d=2 and d=3. Qubit systems are exceptionally simple. Underlying geometry of state spaces and related Lie groups are responsible for that.
We introduce an algebraic measure of correlations in bipartite quantum systems. The proposed quantity, called maximal mutual correlation, provides the information how much a given state differs from the product state of its marginals. In contrast to the entanglement or quantum discord, maximal mutual correlation can be non - zero for some classically correlated quantum states.
In the paper we study the notion of trace norm geometric discord in the system of two qutrits. We compute this quantity for some class of states including qutrit Bell states, Werner states and bound entangled states.
Hilbert - Schmidt and trace norm geometric quantum discord are compared with regard to their behavior during local time evolution. We consider the system of independent two - level atoms with time evolution given by the dissipative process of spontaneous emission. It is explicitly shown that the Hilbert - Schmidt norm discord has nonphysical properties with respect to such local evolution and cannot serve as a reasonable measure of quantum correlations and the better choice is to use trace norm discord as such a measure.
The dynamical creation of entanglement between three-level atoms coupled to the common vacuum is investigated. For the class of bound entangled initial states we show that the dynamics of closely separated atoms generates stationary distillable entanglement of asymptotic states. We also find that the effect of delayed sudden birth of distillable entanglement occurs in the case of atoms separated by a distance comparable with the radiation wavelength.
The dynamics of entanglement between two-level atoms immersed in a common photon reservoir at finite temperature is investigated. It is shown that in the regime of strong correlations there are nontrivial asymptotic states which can be interpreted in terms of thermal generalization of Werner states.
It is shown that even if the linear entropy of mixed two-qubit state is not smaller then 0.457, Bell - CHSH inequalities can be violated. This contradicts the result obtained in the paper of E. Santos [1].
We discuss the influence of a noisy environment on entangled states of two atoms and show that all such states disentangle in finite time.